The hot-electron energy loss rate (ELR) is studied by using the nonequilibrium Green's function approach. The effect due to the anharmonic interaction is considered. As a result, hot electrons lose their energy primarily by creating pairs of acoustic phonons via LO phonons. When acoustic phonons are kept at the lattice temperature, the nonequilibrium distribution for LO phonons is derived by imposing the steady state condition. We show that our result is able to account for the dramatic enhancement of the hot-electron ELR observed in GaAs/GaAlAs semiconductors at low temperatures.PACS numbers: 72.10. Di, 63.20.Hp, 63.20.Ls, 72.20.Ht During recent years intensive experimental [1-7] and theoretical [8][9][10][11][12][13][14] efforts have been devoted to the understanding of the hot electron energy loss rate (ELR) in semiconductors. In the hot-electron energy loss experiments, electrons are heated by an external field. With strong electron-electron interaction, electrons equilibrate among themselves at the temperature TE before giving off energy to phonon systems. It is believed [1][2][3][4][5][6][7][8][9][10][11][12][13][14] that in semiconductors such as GaAs/GaAlAs, electrons lose energy mainly by emitting longitudinal optical (LO) phonons through the Prohlich interaction for TE > 50 K, and by acoustic phonons through the deformation potential interaction below TE < 15 K.The ELR for hot electrons was first calculated by Kogan [8] to describe the energy transfer from hot electrons to LO phonons by employing the second order perturbation theory. It was also studied by Lei and Ting [9] using the Green's function method for hot electrons under a strong electric field. Kogan's formula was modified later by a number of authors [10] to account for the hot-optical-phonon effect by introducing a phenomenological finite energy transfer rate from LO phonons to acoustic phonons. It has been well known that these modified formulas are not able to explain the dramatic enhancement of the ELR observed in the experiment of Shah et al.[4] at low temperatures. In several subsequent publications, Das Sarma and co-workers [11] investigated this problem by simply renormalizing the optical phonon Green's function with electron-phonon interactions. The renormalized LO phonon spectrum consists of the low lying electron-hole-like and plasmonlike excitations. By assuming that these electron-hole-like and plasmonlike excitations are kept at the lattice temperature TL, they found that their ELR [11] exhibits orders of magnitude enhancement at low temperatures over that given by Kogan's formula. However, as Dharma-wardana [12] pointed out recently, the particle-hole-like and plasmonlike excitations exhibited in the LO phonon spectrum of Ref. [11] should be at the electron temperature TE instead of the lattice temperature TE,. When this correction has been taken care of, the enhancement of ELR at low temperatures disappears. Therefore, the underlying physical reason for the low-temperature enhancement of ELR [4] is still unsettled.In the ...